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Speaking as a PM, you've basically highlighted the most important part: management.

The job of a PM isn't to translate fickle external whims into a constantly churning set of priorities. That isn't management. It's reaction. And it's worthless.

A real product manager manages those competing interests and influences, and translates that into a focused, steady set of priorities and an overall direction. And if priorities must change or direction must move, that PM must make those decisions carefully, and must exude a sense of focus and control when doing so.